The chapters in this volume were presented at the July 2005NATO Advanced Study Institute on Advances in Sensing with Security App- cations. The conference was held at the beautiful Il Ciocco resort near Lucca, in the glorious Tuscany region of northern Italy. Once again we gathered at this idyllic spot to explore and extend the reciprocity between mathematics and engineering. The dynamic interaction - tween world-renowned scientists from the usually disparate communities of pure mathematicians and applied scientists which occurred at our six previous ASI's continued at this meeting. The fusion of basic ideas in mathematics, biology, and chemistry with ongoing improvements in hardware and computation o?ers the promise of much more sophisticated and accurate sensing capabilities than c- rently exist. Coupled with the dramatic rise in the need for surveillance in innumerable aspects of our daily lives, brought about by hostile acts deemed unimaginable only a few short years ago, the time was right for scientists in the diverse areas of sensing and security to join together in a concerted e?ort to combat the new brands of terrorism. This ASI was one important initial step. To encompass the diverse nature of the s- ject and the varied backgrounds of the anticipated participants, the ASI was divided into three broadly de?ned but interrelated areas: the - creasing need for fast and accurate sensing, the scienti?c underpinnings of the ongoing revolution in sensing, and speci?c sensing algorithms and techniques. The ASI brought together world leaders from academia, government, andindustry, withextensivemultidisciplinarybackgroundsevidencedby theirresearchandparticipationinnumerousworkshopsandconferences.